Let ,S= {a,b}
S⨉S ={(a,a),(a,b),(b,a),(b,b)}
Largest equivalence relation on S =S⨉S ={(a,a),(a,b),(b,a),(b,b)} because it follows all the three properties Reflaxive ,Symmetric and transitivity and it is the largest set .
Smallest equivalence relation on S ={(a,a),(b,b)} and cardinality is 2.